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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.analysis.polynomials;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.util.ArrayList;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.fraction.BigFraction;<a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    /**<a name="line.23"></a>
<FONT color="green">024</FONT>     * A collection of static methods that operate on or return polynomials.<a name="line.24"></a>
<FONT color="green">025</FONT>     * <a name="line.25"></a>
<FONT color="green">026</FONT>     * @version $Revision: 760901 $ $Date: 2009-04-01 10:29:18 -0400 (Wed, 01 Apr 2009) $<a name="line.26"></a>
<FONT color="green">027</FONT>     * @since 2.0<a name="line.27"></a>
<FONT color="green">028</FONT>     */<a name="line.28"></a>
<FONT color="green">029</FONT>    public class PolynomialsUtils {<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>        /** Coefficients for Chebyshev polynomials. */<a name="line.31"></a>
<FONT color="green">032</FONT>        private static final ArrayList&lt;BigFraction&gt; CHEBYSHEV_COEFFICIENTS;<a name="line.32"></a>
<FONT color="green">033</FONT>    <a name="line.33"></a>
<FONT color="green">034</FONT>        /** Coefficients for Hermite polynomials. */<a name="line.34"></a>
<FONT color="green">035</FONT>        private static final ArrayList&lt;BigFraction&gt; HERMITE_COEFFICIENTS;<a name="line.35"></a>
<FONT color="green">036</FONT>    <a name="line.36"></a>
<FONT color="green">037</FONT>        /** Coefficients for Laguerre polynomials. */<a name="line.37"></a>
<FONT color="green">038</FONT>        private static final ArrayList&lt;BigFraction&gt; LAGUERRE_COEFFICIENTS;<a name="line.38"></a>
<FONT color="green">039</FONT>    <a name="line.39"></a>
<FONT color="green">040</FONT>        /** Coefficients for Legendre polynomials. */<a name="line.40"></a>
<FONT color="green">041</FONT>        private static final ArrayList&lt;BigFraction&gt; LEGENDRE_COEFFICIENTS;<a name="line.41"></a>
<FONT color="green">042</FONT>    <a name="line.42"></a>
<FONT color="green">043</FONT>        static {<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>            // initialize recurrence for Chebyshev polynomials<a name="line.45"></a>
<FONT color="green">046</FONT>            // T0(X) = 1, T1(X) = 0 + 1 * X<a name="line.46"></a>
<FONT color="green">047</FONT>            CHEBYSHEV_COEFFICIENTS = new ArrayList&lt;BigFraction&gt;();<a name="line.47"></a>
<FONT color="green">048</FONT>            CHEBYSHEV_COEFFICIENTS.add(BigFraction.ONE);<a name="line.48"></a>
<FONT color="green">049</FONT>            CHEBYSHEV_COEFFICIENTS.add(BigFraction.ZERO);<a name="line.49"></a>
<FONT color="green">050</FONT>            CHEBYSHEV_COEFFICIENTS.add(BigFraction.ONE);<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>            // initialize recurrence for Hermite polynomials<a name="line.52"></a>
<FONT color="green">053</FONT>            // H0(X) = 1, H1(X) = 0 + 2 * X<a name="line.53"></a>
<FONT color="green">054</FONT>            HERMITE_COEFFICIENTS = new ArrayList&lt;BigFraction&gt;();<a name="line.54"></a>
<FONT color="green">055</FONT>            HERMITE_COEFFICIENTS.add(BigFraction.ONE);<a name="line.55"></a>
<FONT color="green">056</FONT>            HERMITE_COEFFICIENTS.add(BigFraction.ZERO);<a name="line.56"></a>
<FONT color="green">057</FONT>            HERMITE_COEFFICIENTS.add(BigFraction.TWO);<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>            // initialize recurrence for Laguerre polynomials<a name="line.59"></a>
<FONT color="green">060</FONT>            // L0(X) = 1, L1(X) = 1 - 1 * X<a name="line.60"></a>
<FONT color="green">061</FONT>            LAGUERRE_COEFFICIENTS = new ArrayList&lt;BigFraction&gt;();<a name="line.61"></a>
<FONT color="green">062</FONT>            LAGUERRE_COEFFICIENTS.add(BigFraction.ONE);<a name="line.62"></a>
<FONT color="green">063</FONT>            LAGUERRE_COEFFICIENTS.add(BigFraction.ONE);<a name="line.63"></a>
<FONT color="green">064</FONT>            LAGUERRE_COEFFICIENTS.add(BigFraction.MINUS_ONE);<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>            // initialize recurrence for Legendre polynomials<a name="line.66"></a>
<FONT color="green">067</FONT>            // P0(X) = 1, P1(X) = 0 + 1 * X<a name="line.67"></a>
<FONT color="green">068</FONT>            LEGENDRE_COEFFICIENTS = new ArrayList&lt;BigFraction&gt;();<a name="line.68"></a>
<FONT color="green">069</FONT>            LEGENDRE_COEFFICIENTS.add(BigFraction.ONE);<a name="line.69"></a>
<FONT color="green">070</FONT>            LEGENDRE_COEFFICIENTS.add(BigFraction.ZERO);<a name="line.70"></a>
<FONT color="green">071</FONT>            LEGENDRE_COEFFICIENTS.add(BigFraction.ONE);<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        }<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>        /**<a name="line.75"></a>
<FONT color="green">076</FONT>         * Private constructor, to prevent instantiation.<a name="line.76"></a>
<FONT color="green">077</FONT>         */<a name="line.77"></a>
<FONT color="green">078</FONT>        private PolynomialsUtils() {<a name="line.78"></a>
<FONT color="green">079</FONT>        }<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>        /**<a name="line.81"></a>
<FONT color="green">082</FONT>         * Create a Chebyshev polynomial of the first kind.<a name="line.82"></a>
<FONT color="green">083</FONT>         * &lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html"&gt;Chebyshev<a name="line.83"></a>
<FONT color="green">084</FONT>         * polynomials of the first kind&lt;/a&gt; are orthogonal polynomials.<a name="line.84"></a>
<FONT color="green">085</FONT>         * They can be defined by the following recurrence relations:<a name="line.85"></a>
<FONT color="green">086</FONT>         * &lt;pre&gt;<a name="line.86"></a>
<FONT color="green">087</FONT>         *  T&lt;sub&gt;0&lt;/sub&gt;(X)   = 1<a name="line.87"></a>
<FONT color="green">088</FONT>         *  T&lt;sub&gt;1&lt;/sub&gt;(X)   = X<a name="line.88"></a>
<FONT color="green">089</FONT>         *  T&lt;sub&gt;k+1&lt;/sub&gt;(X) = 2X T&lt;sub&gt;k&lt;/sub&gt;(X) - T&lt;sub&gt;k-1&lt;/sub&gt;(X)<a name="line.89"></a>
<FONT color="green">090</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.90"></a>
<FONT color="green">091</FONT>         * @param degree degree of the polynomial<a name="line.91"></a>
<FONT color="green">092</FONT>         * @return Chebyshev polynomial of specified degree<a name="line.92"></a>
<FONT color="green">093</FONT>         */<a name="line.93"></a>
<FONT color="green">094</FONT>        public static PolynomialFunction createChebyshevPolynomial(final int degree) {<a name="line.94"></a>
<FONT color="green">095</FONT>            return buildPolynomial(degree, CHEBYSHEV_COEFFICIENTS,<a name="line.95"></a>
<FONT color="green">096</FONT>                    new RecurrenceCoefficientsGenerator() {<a name="line.96"></a>
<FONT color="green">097</FONT>                private final BigFraction[] coeffs = { BigFraction.ZERO, BigFraction.TWO, BigFraction.ONE };<a name="line.97"></a>
<FONT color="green">098</FONT>                /** {@inheritDoc} */<a name="line.98"></a>
<FONT color="green">099</FONT>                public BigFraction[] generate(int k) {<a name="line.99"></a>
<FONT color="green">100</FONT>                    return coeffs;<a name="line.100"></a>
<FONT color="green">101</FONT>                }<a name="line.101"></a>
<FONT color="green">102</FONT>            });<a name="line.102"></a>
<FONT color="green">103</FONT>        }<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /**<a name="line.105"></a>
<FONT color="green">106</FONT>         * Create a Hermite polynomial.<a name="line.106"></a>
<FONT color="green">107</FONT>         * &lt;p&gt;&lt;a href="http://mathworld.wolfram.com/HermitePolynomial.html"&gt;Hermite<a name="line.107"></a>
<FONT color="green">108</FONT>         * polynomials&lt;/a&gt; are orthogonal polynomials.<a name="line.108"></a>
<FONT color="green">109</FONT>         * They can be defined by the following recurrence relations:<a name="line.109"></a>
<FONT color="green">110</FONT>         * &lt;pre&gt;<a name="line.110"></a>
<FONT color="green">111</FONT>         *  H&lt;sub&gt;0&lt;/sub&gt;(X)   = 1<a name="line.111"></a>
<FONT color="green">112</FONT>         *  H&lt;sub&gt;1&lt;/sub&gt;(X)   = 2X<a name="line.112"></a>
<FONT color="green">113</FONT>         *  H&lt;sub&gt;k+1&lt;/sub&gt;(X) = 2X H&lt;sub&gt;k&lt;/sub&gt;(X) - 2k H&lt;sub&gt;k-1&lt;/sub&gt;(X)<a name="line.113"></a>
<FONT color="green">114</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.114"></a>
<FONT color="green">115</FONT>    <a name="line.115"></a>
<FONT color="green">116</FONT>         * @param degree degree of the polynomial<a name="line.116"></a>
<FONT color="green">117</FONT>         * @return Hermite polynomial of specified degree<a name="line.117"></a>
<FONT color="green">118</FONT>         */<a name="line.118"></a>
<FONT color="green">119</FONT>        public static PolynomialFunction createHermitePolynomial(final int degree) {<a name="line.119"></a>
<FONT color="green">120</FONT>            return buildPolynomial(degree, HERMITE_COEFFICIENTS,<a name="line.120"></a>
<FONT color="green">121</FONT>                    new RecurrenceCoefficientsGenerator() {<a name="line.121"></a>
<FONT color="green">122</FONT>                /** {@inheritDoc} */<a name="line.122"></a>
<FONT color="green">123</FONT>                public BigFraction[] generate(int k) {<a name="line.123"></a>
<FONT color="green">124</FONT>                    return new BigFraction[] {<a name="line.124"></a>
<FONT color="green">125</FONT>                            BigFraction.ZERO,<a name="line.125"></a>
<FONT color="green">126</FONT>                            BigFraction.TWO,<a name="line.126"></a>
<FONT color="green">127</FONT>                            new BigFraction(2 * k)};<a name="line.127"></a>
<FONT color="green">128</FONT>                }<a name="line.128"></a>
<FONT color="green">129</FONT>            });<a name="line.129"></a>
<FONT color="green">130</FONT>        }<a name="line.130"></a>
<FONT color="green">131</FONT>    <a name="line.131"></a>
<FONT color="green">132</FONT>        /**<a name="line.132"></a>
<FONT color="green">133</FONT>         * Create a Laguerre polynomial.<a name="line.133"></a>
<FONT color="green">134</FONT>         * &lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LaguerrePolynomial.html"&gt;Laguerre<a name="line.134"></a>
<FONT color="green">135</FONT>         * polynomials&lt;/a&gt; are orthogonal polynomials.<a name="line.135"></a>
<FONT color="green">136</FONT>         * They can be defined by the following recurrence relations:<a name="line.136"></a>
<FONT color="green">137</FONT>         * &lt;pre&gt;<a name="line.137"></a>
<FONT color="green">138</FONT>         *        L&lt;sub&gt;0&lt;/sub&gt;(X)   = 1<a name="line.138"></a>
<FONT color="green">139</FONT>         *        L&lt;sub&gt;1&lt;/sub&gt;(X)   = 1 - X<a name="line.139"></a>
<FONT color="green">140</FONT>         *  (k+1) L&lt;sub&gt;k+1&lt;/sub&gt;(X) = (2k + 1 - X) L&lt;sub&gt;k&lt;/sub&gt;(X) - k L&lt;sub&gt;k-1&lt;/sub&gt;(X)<a name="line.140"></a>
<FONT color="green">141</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.141"></a>
<FONT color="green">142</FONT>         * @param degree degree of the polynomial<a name="line.142"></a>
<FONT color="green">143</FONT>         * @return Laguerre polynomial of specified degree<a name="line.143"></a>
<FONT color="green">144</FONT>         */<a name="line.144"></a>
<FONT color="green">145</FONT>        public static PolynomialFunction createLaguerrePolynomial(final int degree) {<a name="line.145"></a>
<FONT color="green">146</FONT>            return buildPolynomial(degree, LAGUERRE_COEFFICIENTS,<a name="line.146"></a>
<FONT color="green">147</FONT>                    new RecurrenceCoefficientsGenerator() {<a name="line.147"></a>
<FONT color="green">148</FONT>                /** {@inheritDoc} */<a name="line.148"></a>
<FONT color="green">149</FONT>                public BigFraction[] generate(int k) {<a name="line.149"></a>
<FONT color="green">150</FONT>                    final int kP1 = k + 1;<a name="line.150"></a>
<FONT color="green">151</FONT>                    return new BigFraction[] {<a name="line.151"></a>
<FONT color="green">152</FONT>                            new BigFraction(2 * k + 1, kP1),<a name="line.152"></a>
<FONT color="green">153</FONT>                            new BigFraction(-1, kP1),<a name="line.153"></a>
<FONT color="green">154</FONT>                            new BigFraction(k, kP1)};<a name="line.154"></a>
<FONT color="green">155</FONT>                }<a name="line.155"></a>
<FONT color="green">156</FONT>            });<a name="line.156"></a>
<FONT color="green">157</FONT>        }<a name="line.157"></a>
<FONT color="green">158</FONT>    <a name="line.158"></a>
<FONT color="green">159</FONT>        /**<a name="line.159"></a>
<FONT color="green">160</FONT>         * Create a Legendre polynomial.<a name="line.160"></a>
<FONT color="green">161</FONT>         * &lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LegendrePolynomial.html"&gt;Legendre<a name="line.161"></a>
<FONT color="green">162</FONT>         * polynomials&lt;/a&gt; are orthogonal polynomials.<a name="line.162"></a>
<FONT color="green">163</FONT>         * They can be defined by the following recurrence relations:<a name="line.163"></a>
<FONT color="green">164</FONT>         * &lt;pre&gt;<a name="line.164"></a>
<FONT color="green">165</FONT>         *        P&lt;sub&gt;0&lt;/sub&gt;(X)   = 1<a name="line.165"></a>
<FONT color="green">166</FONT>         *        P&lt;sub&gt;1&lt;/sub&gt;(X)   = X<a name="line.166"></a>
<FONT color="green">167</FONT>         *  (k+1) P&lt;sub&gt;k+1&lt;/sub&gt;(X) = (2k+1) X P&lt;sub&gt;k&lt;/sub&gt;(X) - k P&lt;sub&gt;k-1&lt;/sub&gt;(X)<a name="line.167"></a>
<FONT color="green">168</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.168"></a>
<FONT color="green">169</FONT>         * @param degree degree of the polynomial<a name="line.169"></a>
<FONT color="green">170</FONT>         * @return Legendre polynomial of specified degree<a name="line.170"></a>
<FONT color="green">171</FONT>         */<a name="line.171"></a>
<FONT color="green">172</FONT>        public static PolynomialFunction createLegendrePolynomial(final int degree) {<a name="line.172"></a>
<FONT color="green">173</FONT>            return buildPolynomial(degree, LEGENDRE_COEFFICIENTS,<a name="line.173"></a>
<FONT color="green">174</FONT>                                   new RecurrenceCoefficientsGenerator() {<a name="line.174"></a>
<FONT color="green">175</FONT>                /** {@inheritDoc} */<a name="line.175"></a>
<FONT color="green">176</FONT>                public BigFraction[] generate(int k) {<a name="line.176"></a>
<FONT color="green">177</FONT>                    final int kP1 = k + 1;<a name="line.177"></a>
<FONT color="green">178</FONT>                    return new BigFraction[] {<a name="line.178"></a>
<FONT color="green">179</FONT>                            BigFraction.ZERO,<a name="line.179"></a>
<FONT color="green">180</FONT>                            new BigFraction(k + kP1, kP1),<a name="line.180"></a>
<FONT color="green">181</FONT>                            new BigFraction(k, kP1)};<a name="line.181"></a>
<FONT color="green">182</FONT>                }<a name="line.182"></a>
<FONT color="green">183</FONT>            });<a name="line.183"></a>
<FONT color="green">184</FONT>        }<a name="line.184"></a>
<FONT color="green">185</FONT>    <a name="line.185"></a>
<FONT color="green">186</FONT>        /** Get the coefficients array for a given degree.<a name="line.186"></a>
<FONT color="green">187</FONT>         * @param degree degree of the polynomial<a name="line.187"></a>
<FONT color="green">188</FONT>         * @param coefficients list where the computed coefficients are stored<a name="line.188"></a>
<FONT color="green">189</FONT>         * @param generator recurrence coefficients generator<a name="line.189"></a>
<FONT color="green">190</FONT>         * @return coefficients array<a name="line.190"></a>
<FONT color="green">191</FONT>         */<a name="line.191"></a>
<FONT color="green">192</FONT>        private static PolynomialFunction buildPolynomial(final int degree,<a name="line.192"></a>
<FONT color="green">193</FONT>                                                          final ArrayList&lt;BigFraction&gt; coefficients,<a name="line.193"></a>
<FONT color="green">194</FONT>                                                          final RecurrenceCoefficientsGenerator generator) {<a name="line.194"></a>
<FONT color="green">195</FONT>    <a name="line.195"></a>
<FONT color="green">196</FONT>            final int maxDegree = (int) Math.floor(Math.sqrt(2 * coefficients.size())) - 1;<a name="line.196"></a>
<FONT color="green">197</FONT>            synchronized (PolynomialsUtils.class) {<a name="line.197"></a>
<FONT color="green">198</FONT>                if (degree &gt; maxDegree) {<a name="line.198"></a>
<FONT color="green">199</FONT>                    computeUpToDegree(degree, maxDegree, generator, coefficients);<a name="line.199"></a>
<FONT color="green">200</FONT>                }<a name="line.200"></a>
<FONT color="green">201</FONT>            }<a name="line.201"></a>
<FONT color="green">202</FONT>    <a name="line.202"></a>
<FONT color="green">203</FONT>            // coefficient  for polynomial 0 is  l [0]<a name="line.203"></a>
<FONT color="green">204</FONT>            // coefficients for polynomial 1 are l [1] ... l [2] (degrees 0 ... 1)<a name="line.204"></a>
<FONT color="green">205</FONT>            // coefficients for polynomial 2 are l [3] ... l [5] (degrees 0 ... 2)<a name="line.205"></a>
<FONT color="green">206</FONT>            // coefficients for polynomial 3 are l [6] ... l [9] (degrees 0 ... 3)<a name="line.206"></a>
<FONT color="green">207</FONT>            // coefficients for polynomial 4 are l[10] ... l[14] (degrees 0 ... 4)<a name="line.207"></a>
<FONT color="green">208</FONT>            // coefficients for polynomial 5 are l[15] ... l[20] (degrees 0 ... 5)<a name="line.208"></a>
<FONT color="green">209</FONT>            // coefficients for polynomial 6 are l[21] ... l[27] (degrees 0 ... 6)<a name="line.209"></a>
<FONT color="green">210</FONT>            // ...<a name="line.210"></a>
<FONT color="green">211</FONT>            final int start = degree * (degree + 1) / 2;<a name="line.211"></a>
<FONT color="green">212</FONT>    <a name="line.212"></a>
<FONT color="green">213</FONT>            final double[] a = new double[degree + 1];<a name="line.213"></a>
<FONT color="green">214</FONT>            for (int i = 0; i &lt;= degree; ++i) {<a name="line.214"></a>
<FONT color="green">215</FONT>                a[i] = coefficients.get(start + i).doubleValue();<a name="line.215"></a>
<FONT color="green">216</FONT>            }<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>            // build the polynomial<a name="line.218"></a>
<FONT color="green">219</FONT>            return new PolynomialFunction(a);<a name="line.219"></a>
<FONT color="green">220</FONT>    <a name="line.220"></a>
<FONT color="green">221</FONT>        }<a name="line.221"></a>
<FONT color="green">222</FONT>        <a name="line.222"></a>
<FONT color="green">223</FONT>        /** Compute polynomial coefficients up to a given degree.<a name="line.223"></a>
<FONT color="green">224</FONT>         * @param degree maximal degree<a name="line.224"></a>
<FONT color="green">225</FONT>         * @param maxDegree current maximal degree<a name="line.225"></a>
<FONT color="green">226</FONT>         * @param generator recurrence coefficients generator<a name="line.226"></a>
<FONT color="green">227</FONT>         * @param coefficients list where the computed coefficients should be appended<a name="line.227"></a>
<FONT color="green">228</FONT>         */<a name="line.228"></a>
<FONT color="green">229</FONT>        private static void computeUpToDegree(final int degree, final int maxDegree,<a name="line.229"></a>
<FONT color="green">230</FONT>                                              final RecurrenceCoefficientsGenerator generator,<a name="line.230"></a>
<FONT color="green">231</FONT>                                              final ArrayList&lt;BigFraction&gt; coefficients) {<a name="line.231"></a>
<FONT color="green">232</FONT>    <a name="line.232"></a>
<FONT color="green">233</FONT>            int startK = (maxDegree - 1) * maxDegree / 2;<a name="line.233"></a>
<FONT color="green">234</FONT>            for (int k = maxDegree; k &lt; degree; ++k) {<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>                // start indices of two previous polynomials Pk(X) and Pk-1(X)<a name="line.236"></a>
<FONT color="green">237</FONT>                int startKm1 = startK;<a name="line.237"></a>
<FONT color="green">238</FONT>                startK += k;<a name="line.238"></a>
<FONT color="green">239</FONT>    <a name="line.239"></a>
<FONT color="green">240</FONT>                // Pk+1(X) = (a[0] + a[1] X) Pk(X) - a[2] Pk-1(X)<a name="line.240"></a>
<FONT color="green">241</FONT>                BigFraction[] ai = generator.generate(k);<a name="line.241"></a>
<FONT color="green">242</FONT>    <a name="line.242"></a>
<FONT color="green">243</FONT>                BigFraction ck     = coefficients.get(startK);<a name="line.243"></a>
<FONT color="green">244</FONT>                BigFraction ckm1   = coefficients.get(startKm1);<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>                // degree 0 coefficient<a name="line.246"></a>
<FONT color="green">247</FONT>                coefficients.add(ck.multiply(ai[0]).subtract(ckm1.multiply(ai[2])));<a name="line.247"></a>
<FONT color="green">248</FONT>    <a name="line.248"></a>
<FONT color="green">249</FONT>                // degree 1 to degree k-1 coefficients<a name="line.249"></a>
<FONT color="green">250</FONT>                for (int i = 1; i &lt; k; ++i) {<a name="line.250"></a>
<FONT color="green">251</FONT>                    final BigFraction ckPrev = ck;<a name="line.251"></a>
<FONT color="green">252</FONT>                    ck     = coefficients.get(startK + i);<a name="line.252"></a>
<FONT color="green">253</FONT>                    ckm1   = coefficients.get(startKm1 + i);<a name="line.253"></a>
<FONT color="green">254</FONT>                    coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1])).subtract(ckm1.multiply(ai[2])));<a name="line.254"></a>
<FONT color="green">255</FONT>                }<a name="line.255"></a>
<FONT color="green">256</FONT>    <a name="line.256"></a>
<FONT color="green">257</FONT>                // degree k coefficient<a name="line.257"></a>
<FONT color="green">258</FONT>                final BigFraction ckPrev = ck;<a name="line.258"></a>
<FONT color="green">259</FONT>                ck = coefficients.get(startK + k);<a name="line.259"></a>
<FONT color="green">260</FONT>                coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1])));<a name="line.260"></a>
<FONT color="green">261</FONT>    <a name="line.261"></a>
<FONT color="green">262</FONT>                // degree k+1 coefficient<a name="line.262"></a>
<FONT color="green">263</FONT>                coefficients.add(ck.multiply(ai[1]));<a name="line.263"></a>
<FONT color="green">264</FONT>    <a name="line.264"></a>
<FONT color="green">265</FONT>            }<a name="line.265"></a>
<FONT color="green">266</FONT>    <a name="line.266"></a>
<FONT color="green">267</FONT>        }<a name="line.267"></a>
<FONT color="green">268</FONT>    <a name="line.268"></a>
<FONT color="green">269</FONT>        /** Interface for recurrence coefficients generation. */<a name="line.269"></a>
<FONT color="green">270</FONT>        private static interface RecurrenceCoefficientsGenerator {<a name="line.270"></a>
<FONT color="green">271</FONT>            /**<a name="line.271"></a>
<FONT color="green">272</FONT>             * Generate recurrence coefficients.<a name="line.272"></a>
<FONT color="green">273</FONT>             * @param k highest degree of the polynomials used in the recurrence<a name="line.273"></a>
<FONT color="green">274</FONT>             * @return an array of three coefficients such that<a name="line.274"></a>
<FONT color="green">275</FONT>             * P&lt;sub&gt;k+1&lt;/sub&gt;(X) = (a[0] + a[1] X) P&lt;sub&gt;k&lt;/sub&gt;(X) - a[2] P&lt;sub&gt;k-1&lt;/sub&gt;(X)<a name="line.275"></a>
<FONT color="green">276</FONT>             */<a name="line.276"></a>
<FONT color="green">277</FONT>            BigFraction[] generate(int k);<a name="line.277"></a>
<FONT color="green">278</FONT>        }<a name="line.278"></a>
<FONT color="green">279</FONT>    <a name="line.279"></a>
<FONT color="green">280</FONT>    }<a name="line.280"></a>




























































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